I had them on my VS '62 Precision ( bought new in April 1983) when they were still labeled "Old Originals". That bass is VERY thin front-to-back. No problem at all except I didn't like the strings. Lottsa thump bur not enough note definition. Had them on for months, tried something else, tried the same set again. Finally gave them to s friend after about five years. That bass has had the same set of GHS Precision flats on it for at least five years. Perfect for me with all the essential thump of the LaBellas and a precise note. I play bass, not a kick drum.
You shouldn't have any problem as long as you know how to properly adjust a truss rod- pre-stress the neck and only snug the nut instead of expecting the nut to do all the work.
John